System and method for soc estimation of a battery

ABSTRACT

The present invention provides a SOC estimation method applied to a battery system comprising a battery pack. The SOC estimation method comprises the steps of: determining an initial SOC value; determining whether the battery pack is in a working status; measuring the voltage and current of the battery pack if the battery pack is in the working status; calculating a current SOC value by using an ampere-hour method based on the initial SOC value and the measured voltage and current; determining dynamic characteristic parameters of the battery pack; and optimizing the current SOC value by using extended Kalman filter (EKF) method and based on the dynamic characteristic parameters of the battery pack.

TECHNICAL FIELD

The present invention is related to Li-ion battery management systems,and more particularly to a system and method for state of charge (SOC)estimation of Li-ion batteries.

BACKGROUND

As the energy-saving and environmental issues have become increasinglyprominent, lithium ion (Li-ion) battery, due to its advantages of highspecific energy and green environmental protection, have been widelyused as large capacity power supply in various fields such aselectronic-powered automotive, aerospace, ship gradually. With thedevelopment of li-ion battery technology, energy density of li-ionbattery becomes higher and higher, quantity of battery units in abattery pack also becomes larger and larger. After long-time use of abattery pack, asymmetry developed among the batteries in the batterypack can cause one or more of the batteries overcharging orover-discharging, and subsequently lowers the performance of the batterypack in the whole, resulting in serious effect on the service life ofthe battery pack. Therefore, a battery management system for managingand monitoring the working state of the battery pack is indispensable.

In practice, state of charge (SOC) is an important reference parameterof the working state of the li-ion battery pack, and is usually employedto indicate remainder energy of the li-ion battery pack. Accurate SOCestimation of the li-ion battery pack utilized in automobiles can notonly tell drivers of correct estimated mileage of the automobiles, butalso ensure charging/discharging optimization of the li-ion batterypack, which ensures safe utility of the li-ion battery pack. When theautomobile is running, large currents may cause the battery pack to beoverly discharged and subsequently destroy the battery pack. Therefore,real time collection of voltage, temperature, and charging/dischargingcurrent of each battery is important for accurate SOC estimation of thebattery so as to prolong the life of the battery pack and increaseperformance of the automobile.

The SOC can be estimated based on attribute parameters such as voltage,current, resistance, temperature of the battery. The attributeparameters of the battery generally can change in accordance with theaging of the battery and other uncertain factors, such as random roadconditions the automobile is going through.

Currently, the most popular method for SOC estimation of battery is theso-called ampere-hour method, which is also a relatively accurate methodon SOC estimation. The ampere-hour method employs real time currentintegral to calculate ampere hour, and then revises temperature,self-discharging data and ageing parameters that can affect the SOCestimation, and eventually obtains a relatively accurate SOC value byusing a revision function and said parameters. However, theabove-mentioned method is still far from being sufficient for practicalsituations because there are many other factors that could practicallyaffect SOC estimation of the battery, and because it is hard to achievethe revision function in practice. Therefore, to date the SOC valueestimated by employing the ampere-hour method can be far from the realSOC value of the battery. Other existing methods for SOC estimationinclude constant current/voltage method, open circuit voltage method,specific density method, and so on. These methods each have more or lessdefects that would lead to inaccurate SOC value. Therefore, a novelmethod needs to be developed for accurate SOC estimation of a batterypack.

BRIEF DESCRIPTION OF THE DRAWINGS

The details as well as other features and advantages of this inventionare set forth in the remainder of the specification and are shown in theaccompanying drawings.

FIG. 1 is a schematic diagram of a battery system device including abattery management system according to embodiments of the presentdisclosure.

FIG. 2 is a schematic diagram of the battery management system accordingto a preferred embodiment.

FIG. 3 is a flowchart of a method for obtaining parameters of a secondorder RC equivalent circuit simulating the battery unit in accordancewith an exemplary disclosure of the present invention.

FIG. 4A is an exemplary second order RC equivalent circuit simulatingthe battery unit.

FIG. 4B shows the curve line of voltage changes corresponding to thedischarging currents with time elapsing.

FIG. 4C shows a fitting curve representing values of U_(ed) of FIG. 4Aafter the discharge current being removed.

FIG. 4D shows a fitted voltage loaded upon the series circuit composedof the capacitance-resistance segment of electrochemical polarizationand the capacitance-resistance segment of concentration polarization ofFIG. 4A.

FIG. 5 is a flow chart of SOC estimation method of the battery pack inuse according to a preferred embodiment of the present disclosure.

FIG. 6 is an exemplary OCV-SOC mapping table.

DETAILED DESCRIPTION OF THE EMBODIMENTS

In the following description, for purposes of explanation and notlimitation, specific details are set forth such as particulararchitectures, interfaces, techniques, etc. in order to provide athorough understanding of the present invention. However, it will beapparent to those skilled in the art that the present invention may bepracticed in other embodiments that depart from these specific details.In other instances, detailed descriptions of well-known devices,circuits, and methods are omitted so as not to obscure the descriptionof the present invention with unnecessary detail.

In the exemplary embodiment of the present invention, a battery systemdevice 100, such as an electric bicycle, an electric vehicle or anintegrated power storage system, generally comprises a battery pack 101,a battery management system (BMS) 102 for managing the battery pack 101,and a load 103 powered by the battery pack 101. In the preferredembodiment of the present invention, the battery pack 101 may compriseonly one single battery, or is composed of many batteries seriallyconnected one by one. In the condition that the battery pack 101comprises just one battery, the battery pack 101 can also be calledbattery 101. For consistency, in this embodiment, a single battery ismarked as a battery unit, therefore, the battery pack 101 may compriseone or more battery units. The battery management system 102 is used tomanage and maintain the battery pack 101, comprising but not limited toproviding over-voltage and/or over-current protection, state of charge(SOC) estimation of the battery pack 101. In the exemplary embodiment,the battery pack 101 and the battery management system 102 collectivelyform a power system 10 of the battery system device 100. The load 103may be any kind of power consumption device, such as motors employed bythe electric bicycle or the electric vehicle. In the exemplaryembodiment, the battery pack 101 or the battery unit describedhereinafter is lithium ion (Li-ion) typed.

FIG. 2 is a detailed description of the battery management system 102.In the preferred embodiment of the present disclosure, the batterymanagement system 102 comprises a controller 1020, a storage unit 1021,a measurement module 1022, a balance module 1023, a power supply 1024, acommunication module 1025, and a protection module 1026. In a preferredembodiment, the measurement module 1022, the communication module 1025and the protection module 1026 are electronically connected to thecontroller 1020 by way of photoelectric coupling isolation circuits(PCIC), respectively.

In the preferred embodiment, the storage unit 1021 may be a memoryintegrated with the controller 1020, such as a flash memory, a staticrandom access memory (SRAM), an electrically erasable programmableread-only memory (EEPROM). In other embodiments, the storage unit 1021may be those storage apparatuses independent from but electricallyconnected to the controller 1021, such as a solid state disk or a microhard disk. In alternative embodiments, the storage unit 1021 may be thecombination of the memory and the storage apparatus. The storage unit1021 stores program codes that can be executed by the controller 1021 tomaintain the battery pack 101, for example, estimating the SOC of thebattery pack 101. The storage unit 1021 is also used to store datagenerated during the SOC estimation in accordance with the preferredembodiment of the present invention.

In an exemplary embodiment, the controller 1020 is the PIC18F458 typechip produced by Microchip Technology Incorporation. The PIC18F458 typechip is an 8-bit micro-controller with 32 Kilobytes memory space forstoring program codes, 1536 bytes-sized SRAM and 256 bytes-sized EEPROM.The PIC18F458 type chip further comprises a clock with frequency up to32 MegaHz, which can operate as an external crystal oscillator circuitfor, such as timing. Another outstanding feature of the PIC18F458 typechip is that the power consumption of the chip is relatively low. Forexample, under a sleeping mode, current consumed by the chip is only 0.2μA.

The measurement module 1022 is an important part of the batterymanagement system 102, and is used for measuring parameters such ascurrent, voltage, and temperature of the battery pack 101. The measuredparameters are not only basis for the SOC estimation, but securityguarantee of the battery pack 101. In this disclosure, the currentmeasurement comprises measuring the current flowing through the batterypack 101. The voltage measurement comprises measuring the voltage of thebattery pack 101, and the voltage of each battery unit in the batterypack 101, providing the battery pack 101 comprises more than one batteryunits. The temperature measurement comprises measuring the temperatureof the battery units in the battery pack 101. In this embodiment, themeasured current, voltage and temperature data are stored in the storageunit 1021.

The balance module 1023 is used for balancing the charging/dischargingcurrent of the battery pack 101. In an exemplary embodiment, thebalancing module 1023 comprises monitoring chip LTC6803 and otheraccompanied circuits provided by Linear Technology Corporation.

The power supply 1024 is used for providing various reference voltagesto different function modules, such as the controller 1021, themonitoring chip LTC6803, etc. In this embodiment, the power supply 1024employs the LM2009 chip to provide fixed voltage, such as 15V, and usesother DC/DC regulator, such as LM7805 chip, to convert the fixed 15Vvoltage to various DC outputs, such as 10V, 5V, and provides theconverted DC outputs to the different function modules.

The communication module 1025 provides communication services forabove-mentioned function modules. The communication services comprise aserial peripheral interface (SPI), a controller area network (CAN), andserial communication.

The protection module 1026 provides protections under the conditionssuch as over-current, over-voltage, under-voltage, to ensure normaloperation of the battery system device 100, especially the battery pack101.

In the preferred embodiment of the present invention, before the SOCestimation of the battery pack 101, electrochemical parameters of thebattery pack 101 should be obtained.

1. Obtaining Electrochemical Parameters of the Battery Pack

The electrochemical performance of the battery unit in the battery pack101 generally presents non-linear characteristic. In the preferreddisclosure of the present invention, a second order RC equivalentcircuit is employed to simulate the battery unit, in that the secondorder RC equivalent circuit owns the benefits comprising, for example,the order is relatively low, and parameters thereof are easily to beobtained. Particularly, the second order RC equivalent circuit can beeasily constructed and preferably simulates dynamic characteristics ofthe battery unit under working status. The dynamic characteristicscomprise an ohmic resistance R₀, an electrochemical polarizationresistance R_(e), an electrochemical polarization capacitor C_(e), aconcentration polarization resistance R_(d) and a concentrationpolarization capacitor C_(d). By using certain methods acted on thebattery unit, the dynamic characteristics can be achieved to describethe electrochemical characteristics of the battery unit, subsequently toaid to estimate the state of charge of the battery unit in the batterypack 101.

FIG. 3 is a flowchart of a method for obtaining parameters of the secondorder RC equivalent circuit simulating the battery unit in accordancewith an exemplary disclosure of the present invention. At step S301, thesecond order RC equivalent circuit simulating the battery unit isconstructed, as illustrated in FIG. 4A. The constructed second order RCequivalent circuit comprises the ohmic resistance R₀, theelectrochemical polarization resistance R_(c), the electrochemicalpolarization capacitor C_(c), the concentration polarization resistanceR_(d) and the concentration polarization capacitor C_(d). In theexemplary embodiment, the electrochemical polarization resistance R_(e),the electrochemical polarization capacitor C_(e) are connected inparallel to form a capacitance-resistance segment of electrochemicalpolarization, and the concentration polarization resistance R_(d) andthe concentration polarization capacitor C_(d) are connected in parallelto form a capacitance-resistance segment of concentration polarization.The ohmic resistance R₀, the capacitance-resistance segment ofelectrochemical polarization, and the capacitance-resistance segment ofconcentration polarization are connected in series. In this embodiment,values of the ohmic resistance R₀, the electrochemical polarizationresistance R_(e), the electrochemical polarization capacitor C_(e), theconcentration polarization resistance R_(d) and the concentrationpolarization capacitor C_(d) would be obtained by an experimentalmethod. In the exemplary embodiment, the experimental method comprisesthe following steps:

Step I: keeping the battery unit under a status without charging ordischarging over one hour;

Step II: discharging the battery unit continuously lasting for 900seconds;

Step III: keeping the battery unit under the status without charging ordischarging for a relatively long time, such as one hour, up to the endof the experiment.

FIG. 4B shows the curve line of voltage changes corresponding to thedischarging currents with time elapsing.

1.1 Identifying R₀

In the exemplary embodiment, firstly, placing one battery unit under astatus without charging or discharging over one hour; then loading adischarge current pulse on a positive electrode and a negative electrodeof the battery unit, for example, at the time point of 1800 s shown inFIG. 4B. When the discharge current pulse is loaded, a responsivevoltage upon between the positive electrode and the negative electrodeof the battery unit gets a downward mutation. After continuousdischarging for 900 s, at the time point of the 2700 s shown in FIG. 4B,the discharge current pulse is removed, and the responsive voltage uponthe positive electrode and the negative electrode of the battery unitgets a upward mutation. In the exemplary disclosure, the status withoutcharging or discharging of the battery could be defined as an idlestatus of the battery unit.

Based on the second order RC equivalent circuit simulating the batteryunit, the voltage upon the capacitance-resistance segment ofconcentration polarization composed of the concentration polarizationresistance R_(d) and the concentration polarization capacitor C_(d)could not get a mutation, due to the exist of the concentrationpolarization capacitor C_(d). In the same way, due to the exist of theelectrochemical polarization capacitor C_(c), the voltage upon thecapacitance-resistance segment of electrochemical polarization composedof the electrochemical polarization resistance R_(e) and theelectrochemical polarization capacitor C_(e) also could not get amutation. Therefore, the downward mutation and the upward mutation canonly be caused by the ohmic resistance R₀. According to theabove-mentioned theory, at step S303, the resistance value R₀ of theohmic resistance R₀ can be calculated by dividing the voltage change bythe discharge current, that is, R₀=ΔU/I_(t).

1.2 Identifying τ_(e) and τ_(d)

In the exemplary disclosure, time constants of thecapacitance-resistance segment of electrochemical polarization and thecapacitance-resistance segment of concentration polarization arerespectively represented by τ_(e) and τ_(d), wherein τ_(e)=R_(e)*C_(e),τ_(d)=R_(d)*C_(d).

As shown in FIG. 4B, after the time point of 2700 s, the dischargecurrent pulse is removed, the voltage upon the ohmic resistance R₀ wouldbecome 0 due to no currents flowing through the ohmic resistance R₀. Theupward mutation of the voltage upon the positive electrode and thenegative electrode of the battery unit, as shown in FIG. 4B, is causedby electronic discharging of the capacitors C_(d) and C_(e), which arecharged when the battery unit is discharging. When the capacitors C_(d)and C_(e) discharge completely, the voltage upon the positive electrodeand the negative electrode of the battery unit becomes stable at, forexample, about 4.05 v as shown in FIG. 4B.

After the discharge current pulse being removed, the voltage upon thepositive electrode and the negative electrode of the battery unit isclose to electromotive force of the battery unit. In an exemplarydisclosure, supposing the time point t of removing the discharge currentpulse is zero time, the voltage response upon the positive electrode andthe negative electrode of the battery unit at the time point t could bedeemed as zero state response:

$\begin{matrix}{{u(t)} = {{U_{oc} - U_{ed}} = {U_{oc} - \left( {{U_{d}^{\frac{t}{\tau_{d}}}} + {U_{e}^{\frac{t}{\tau_{e}}}}} \right)}}} & \left( {1\text{-}1} \right)\end{matrix}$

Here, U_(d) and U_(e) respectively stand for voltages loaded upon thecapacitors C_(d) and C_(e), U_(ed) represents the voltage loaded uponthe series circuit composed of the capacitance-resistance segment ofelectrochemical polarization and the capacitance-resistance segment ofconcentration polarization. FIG. 4C shows a fitting curve representingvalues of U_(ed) after the discharge current being removed. At stepS305, with the MATLAB software provided by the MathWorks company, τ_(e)and τ_(d) can be achieved by using the exponent curve fitting module inthe MATLAB software.

1.3 Identifying R_(d) and R_(e)

According to the above-mentioned description, at the time point of 1800s shown in FIG. 4B, the voltage upon the positive electrode and thenegative electrode of the battery unit declines due to the ohmicresistance R₀, the capacitance-resistance segment of electrochemicalpolarization and the capacitance-resistance segment of concentrationpolarization. Because the battery unit has been place at the idle statusfor a long time period, such as over one hour, the capacitor C_(e) inthe capacitance-resistance segment of electrochemical polarization andthe capacitor C_(d) in the capacitance-resistance segment ofconcentration polarization could be deemed as zero electron state. In anexemplary disclosure, supposing the time point t of loading thedischarge current pulse is zero time, voltage response of the capacitorC_(e) and C_(d) to the discharge current pulse is a zero state response:

$\begin{matrix}{{U(t)} = {{U_{oc} - U_{red}} = {U_{oc} - {I\left\lbrack {{R_{d}\left( {1 - ^{\frac{t}{\tau_{d}}}} \right)} + {R_{e}\left( {1 - ^{\frac{t}{\tau_{e}}}} \right)}} \right\rbrack} - {I\; R_{0}}}}} & {1\text{-}2}\end{matrix}$

The voltage U_(ed) loaded upon the series circuit composed of thecapacitance-resistance segment of electrochemical polarization and thecapacitance-resistance segment of concentration polarization is fittedas shown in FIG. 4D. At step S307, putting the calculated τ_(e) andτ_(d) into the formula 1-2, and by using the exponent curve fittingmethod of the MATLAB software, the R_(d) and R_(e) can be achieved.

1.4 Identifying C_(d) and C_(e)

At step S309, based on the formula τ=R*C, it can be concluded that C isequal to τ/R. Because the time constants τ_(e) and τ_(d), the resistancevalues R_(d) and R_(e) of the polarization resistances R_(d) and R_(e)are achieved, it is easy to achieve values C_(d) and C_(e) of thepolarization capacitors C_(d) and C_(e).

In the preferred embodiment of the disclosure, the second order RCequivalent circuit is used to simulate the battery unit. Therefore, theidentified parameters of the second order RC equivalent circuit areindeed dynamic characteristic paramters of the battery unit. Accordingto above-described identifying processes, in one embodiment of thepresent disclosure, identified dynamic characteristic parameters of oneexemplary battery unit are shown in following table:

Parameter Identified value R₀ 34.5 mΩ R_(d) 21.45 mΩ R_(e) 10.6 mΩ C_(d)4768.74 F C_(e) 3678.21 F

In the preferred embodiment, the parameters of the second order RCequivalent circuit simulating the battery unit which are identified byway of said-mentioned method are stored in the storage unit 1021, andwould be invoked in estimating processed when the battery unit is usedin practice.

2. SOC Estimation of the Battery Pack in Use

FIG. 5 is a flow chart of SOC estimation method of the battery pack 101in use according to a preferred embodiment of the present disclosure,which could be applied to the battery system device 100 of FIG. 1. Forexample, the SOC estimation method could be realized by the controller1020 executing the programmed codes stored in the storage unit 1021. Inthe preferred embodiment, the SOC estimation method is periodicallyexecuted by the controller 1020 to achieve a relatively accurate SOC ofthe battery pack 101 in different time points. A time cycle the methodbeing executed periodically could be, for example, 10 millisecond (ms).In other embodiment, the time period could be set or configured as othervalue, such 15 ms. In the preferred embodiment, an once-throughoperation of the SOC estimation method is described as one SOCestimation process.

In the exemplary embodiment, the clock in the controller 1020 wouldrecord the time duration of the battery pack 101 being in the idle statein which there is no charging or discharging occurred to the batterypack 101. For simplicity of description, the time duration of thebattery pack 101 in the idle state is simplified as an idle time of thebattery pack 101. At the beginning of each SOC estimation process, someprogram codes would be executed to determine whether the idle time ofthe battery pack 101 is longer than a predefined time period, such asone hour, at step S501.

If the idle time of the battery pack 101 is not longer than thepredefined time period, at step S502A, the controller 1020 reads aprevious SOC value (here marked as SOC_((k-1))) generated during aprevious SOC estimation process, and regards the SOC_((k-1)) as aninitial SOC value of a current SOC estimation process.

In the preferred embodiment of the present invention, if the batterypack 101 is in the idle state for a relatively long time, for example,over one hour, an open circuit voltage (OCV) of the battery pack 101 issubstantially equal to an electromotive force of the battery pack 101.Therefore, if the idle time of the battery pack 101 is longer than thepredefined time period, at step S502B, the measurement module 1022measures a current voltage upon the positive electrode and the negativeelectrode of the battery pack 101, subsequently, the controller 1020queries an OCV-SOC mapping table to determine a SOC value correspondingto the current voltage, and records the determined SOC value asSOC_((k-1)). The SOC_((k-1)) would act as an initial SOC value of acurrent SOC estimation process.

It should be noted, step S502A and step S502B are alternative in one SOCestimation process according to a preferred embodiment of the presentinvention.

In the preferred embodiment, the OCV-SOC mapping table is established byan experimental method. The experiment method for establishing theOCV-SOC mapping table comprises the steps of:

A) charging the battery pack 101, fully and completely;

B) placing the battery pack 101 in the idle status, without charging ordischarging, for over one hour;

C) discharging the battery pack 101 to reduce 5 percent of the SOC ofthe battery pack 101 by using a programmable electronic load, recordingthe open circuit voltage of the battery pack 101 and subsequentlyplacing the battery pack 101 in the idle state for over one hour;

D) repeating said step C), under constant temperature of substantially20 degree Celsius, until the battery pack 101 discharges completely;

E) establishing the OCV-SOC mapping table based on the recorded opencircuit voltage and corresponding SOC of the battery pack 101.

In this exemplary disclosure, the programmable electronic load employsChroma 6310A type programmable DC electronic load provided by ChromaCompany. FIG. 6 is an exemplary OCV-SOC mapping table of an 18650 typeli-ion battery, which is obtained by using the experiment method forestablishing the OCV-SOC mapping table.

At step S503, the controller 1020 determines whether the battery pack101 is in a working status. In the exemplary disclosure, the workingstatus is opposite to the idle status, that is, the working status meansthe battery pack 101 is discharging and/or charging. In other words, thecontroller 1020 determines the batter pack 101 is in the working statusif the battery pack 101 is discharging and/or charging. If the batterypack 101 is not in the working status, or is in the idle status, theflow returns to step S501 to determine whether an idle time of thebattery pack 101 is longer than the predefined time period in anotherSOC estimation process.

If the battery pack 101 is in the working status, at step S504, themeasurement module 1022 measures current I_((k)) flowing through andvoltage U_((k)) upon the two polarities of the battery pack 101. In thepreferred embodiment of the present disclosure, when measuring thecurrent I_((k)), a direction of the measured current I_((k)) shows thedischarging or charging status of the battery pack 101. Hereinafter, ifthe battery pack 101 is discharging, the current I_((k)) is positive,and if the battery pack 101 is charging, the current I_((k)) isnegative.

At step S505, an ampere hour method is employed to estimate SOC_((k)) incurrent SOC estimation process, based on the determined SOC_((k-1)) instep S502A or S502B.

2.1 Ampere Hour Method

The ampere hour method is also called current integration method, whichis a fundamental method to measure the SOC of batteries. In current SOCestimation process, after determining the SOC_((k-1)) in step S502A orS502B, the battery pack 101 is charging or charging from time point k-1to k, such as 10 ms, a change of the SOC of the battery pack 101 couldbe represented as:

$\begin{matrix}{{\Delta \; {SOC}} = {\frac{1}{Q_{0}}{I(k)}T}} & \left( {2\text{-}1} \right)\end{matrix}$

Here, Q₀ is a total quantity of electric discharge in fixed current of0.1*C of the battery pack 101, wherein C represents the nominal capacityof the battery pack 101. I_((k)) represents the charging or dischargingcurrent of the battery pack 101, wherein I_((k)) is positive if thebattery pack 101 is discharged, otherwise the I_((k)) is negative.

Peukert proposes an empirical formula to revise the SOC of the batterypack 101 working with changing currents, as shown in following formula2-2:

I^(n) *t=K   (2-2)

Here, I represents discharging current, t is a discharging time length,n and K are constants that are determined by types and active materialsof the battery pack 101. In the exemplary disclosure, the activematerial is lithium.

By multiplying two sides of the formula 2-2 by I^(1-n), a new expressionis obtained:

Q=I*t=I ^(l-n) *K   (2-3)

Here, if I=I₀=0.1*C, Q is equal to Q₀ mentioned above; if I=0.5*C, Q ismarked as Q1. According to expression 2-3, Q₀=I₀ ^(1-n)*K, Q₁=I^(1-n)*K.Therefore, Q₁/Q₀=(I/I₀)^(1-n). Assuming Q₁/Q₀=η, Q1=η*Q₀. If k_(η)=1/η,an initial SOC estimation value SOC*_((k)) considering charge/dischargerate is:

SOC*_((k))=SOC_((k-1)) −k _(η) *I(k)*T/Q ₀   (2-4)

Here, k_(η) is a revise value to the capacity volume of the battery pack101. SOC*_((k)) is an initial estimation of the SOC of the battery pack101 by using the ampere-hour method, which would be further corrected inthe following descriptions.

2.2 Recursive Least Square (RLS) Method

At step S506, a recursive least square (RLS) method is employed to,based on parameters R_(o(k-1)), R_(e(k-1)), C_(e(k-1)), R_(d(k-1)),C_(d(k-1)) obtained in the previous SOC estimation process and thevoltage U_((k)) and the current I_((k)) measured at step S504, reviseand achieve another set of parameters R_(o(k)), R_(e(k)), C_(e(k)),R_(d(k)), C_(d(k)) at the current time point k in the current SOCestimation process. The parameters R_(o(k-1)), R_(e(k-1)), C_(e(k-1)),R_(d(k-1)), C_(d(k-1)) obtained in the previous SOC estimation processare stored in the storage unit 1021. If it is a first SOC estimationprocess when the battery pack 101 is in use, the R_(o(k-1)), R_(e(k-1)),C_(e(k-1)), R_(d(k-1)), C_(d(k-1)) would be those parameters identifiedaccording to the method described in FIG. 3.

Based on the battery model shown in FIG. 4A, and according to Kirchhofflaws and Laplace transform, it could be drawn upon changing time domaint to Laplace domain s:

$\begin{matrix}{{U(s)} = {{I(s)}\left( {R_{0} + \frac{R_{e}}{1 + {R_{e}C_{e}s}} + \frac{R_{d}}{1 + {R_{d}C_{d}s}}} \right)}} & \left( {2\text{-}5} \right)\end{matrix}$

Here, the most right part of the formula is defined as battery transferfunction:

$\begin{matrix}{{G(s)} = {R_{0} + \frac{R_{e}}{1 + {\tau_{e}s}} + \frac{R_{d}}{1 + {\tau_{d}s}}}} & \left( {2\text{-}6} \right)\end{matrix}$

The battery transfer function 2-6 could be transformed to a discreteform as following expression 2-7 by way of the bilinear transformationmethod:

$\begin{matrix}{{G\left( z^{- 1} \right)} = \frac{\beta_{0} + {\beta_{1}Z^{- 1}} + {\beta_{2}Z^{- 2}}}{1 + {\alpha_{1}Z^{- 1}} + {\alpha_{2}Z^{- 2}}}} & \left( {2\text{-}7} \right)\end{matrix}$

An difference equation of the expression 2-7 could be expressed asfollowing:

U(k)=−α₁ U(k−1)−α₂ U(k−2)+β₀ I(k)+β₁ I(k−1)+β₂ I(k−2)   (2-8)

Here, given θ=[α₁ α₂ β₀ β₁ β₂], h^(T)(k)=[−U(k−1)−U(k−2) I(k) I(k−1)I(k−2)], it can be concluded:

U(k)=h ^(T)(k)θ+e(k)   (2-9)

Expression 2-10 shows fundamental algorithm of the recursive leastsquare (RLS) method:

$\begin{matrix}\left\{ \begin{matrix}{{\hat{\theta}(k)} = {{\hat{\theta}\left( {k - 1} \right)} + {{K(k)}\left\lbrack {{y(k)} - {{h^{T}(k)}{\hat{\theta}\left( {k - 1} \right)}}} \right\rbrack}}} \\{{K(k)} = {{P\left( {k - 1} \right)}{{h(k)}\left\lbrack {{{h^{T}(k)}{P\left( {k - 1} \right)}{h(k)}} + \lambda} \right\rbrack}^{- 1}}} \\{{P(k)} = {{\frac{1}{\lambda}\left\lbrack {I - {{K(k)}{h^{T}(k)}}} \right\rbrack}{P\left( {k - 1} \right)}}}\end{matrix} \right. & \left( {2\text{-}10} \right)\end{matrix}$

Here, K_((k)) is a gain factor, P_((k-1)) represents a covariance matrixupon the (k−1)_(th) measurement. In the preferred embodiment of thepresent disclosure, the K_((k)) is set as 5, and P_((k-1)) is equal toαI_(n), wherein α is a giant number and is set as 10⁵ in thisdisclosure, I_(n) is an identity matrix of size n, which is the n×nsquare matrix, with matrix elements being ones on the main diagonal andzeros elsewhere.

According to the formula (2-10), {circumflex over (θ)}(k) could becalculated, which could be regarded as a current θ. Because θ=[α₁ α₂ β₀β₁ β₂], α₁, α₂, β₀, β₁, β₂ could be subsequently obtained.

Putting α₁, α₂, β₀, β₁, β₂ into an inverse equation 2-11, the parametersR_(o(k)), R_(e(k)), C_(e(k)), R_(d(k)), C_(d(k)) at the current timepoint k in the current SOC estimation process could be achieved. In theinverse equation 2-11, T is a sampling cycle, which is the time intervalof the RLS method being executed.

$\begin{matrix}\left\{ \begin{matrix}{R_{0} = \frac{\beta_{0} - \beta_{1} + \beta_{1}}{1 - \alpha_{1} + \alpha_{2}}} \\{{\tau_{e}\tau_{d}} = \frac{T^{2}\left( {1 - \alpha_{1} + \alpha_{2}} \right)}{4\left( {1 + \alpha_{1} + \alpha_{2}} \right)}} \\{{\tau_{e} + \tau_{d}} = \frac{T\left( {1 - \alpha_{2}} \right)}{1 + \alpha_{1} + \alpha_{2}}} \\{{R_{0} + R_{e} + R_{d}} = \frac{\beta_{0} - \beta_{1} + \beta_{1}}{1 + \alpha_{1} + \alpha_{2}}} \\{{{R_{0}\tau_{e}} + {R_{0}\tau_{d}} + {R_{e}\tau_{d}} + {R_{d}\tau_{e}}} = \frac{T\left( {\beta_{0} - \beta_{1}} \right)}{1 + \alpha_{1} + \alpha_{2}}}\end{matrix} \right. & \left( {2\text{-}11} \right)\end{matrix}$

The achieved parameters R_(o(k)), R_(e(k)), C_(e(k)), R_(d(k)), C_(d(k))are stored in the storage unit 1021, and used as basis of a next SOCestimation process.

At step S507, SOC*_((k)) obtained at step S505 would be revised by usingthe parameters R_(o(k)), R_(e(k)), C_(e(k)), R_(d(k)), C_(d(k)) achievedat step S506 in light of extended kalman filter (EKF) method.

2.3 Extended Kalman Filter (EKF) Method

Equation of state employed by the EKF method in the preferred embodimentcould be expressed as following:

X _(k) =A _(k) X _(k-1) +B _(k) I _(k) +W _(k)   (2-12)

Here, X_(k) stands for a variable of state, A_(k) represents a gainmatrix of the variable of state at the time point k, B_(k) represents again matrix of an input variable at the time pint k, I_(k) is the inputvariable at the time point k, W_(k) means process noises.

An observer output equation of the EKF method is:

Y _(k) =C _(k) X _(k) +Z _(k)   (2-13)

Here, Y_(k) is an observer output vector, C_(k) is a transfer matrix ofthe variable of state at the time point k, Z_(k) means system observingvalue at the time point k.

A state space equation employed by the EKF method is as followingexpression:

$\begin{matrix}\left\{ \begin{matrix}{{{SOC}(k)} = {{{SOC}^{*}(k)} - {\frac{k_{\eta}T}{Q_{0}}{I(k)}}}} \\{{U_{e}(k)} = {{^{- \frac{T}{\tau_{e}{({k - 1})}}}{U_{e}\left( {k - 1} \right)}} + {\left( {1 - ^{- \frac{T}{\tau_{e}{({k - 1})}}}} \right){R_{e}\left( {k - 1} \right)}{I(k)}}}} \\{{U_{e}(k)} = {{^{- \frac{T}{\tau_{e}{({k - 1})}}}{U_{e}\left( {k - 1} \right)}} + {\left( {1 - ^{- \frac{T}{\tau_{d}{({k - 1})}}}} \right){R_{d}\left( {k - 1} \right)}{I(k)}}}}\end{matrix} \right. & \left( {2\text{-}14} \right)\end{matrix}$

Here, SOC*_((k)) obtained at step S505 would be served as an input ofthe expression 2-14.

In the expression 2-14, U_(e) and U_(d) are voltages respectively loadedupon the capacitors C_(e) and C_(d), I_((k)) is the current obtained atthe measurement step S504.

In the exemplary embodiment of the present disclosure, the method forrevising the SOC*_((k)) by using the EKF method comprises the followingsteps:

Step 1: Determining the Linear Coefficient of the Variable of State

Based on the parameters R_(o(k)), R_(e(k)), C_(e(k)), R_(d(k)), C_(d(k))achieved at step S506, one can compute τ_(e) and τ_(d). Then, thefollowing coefficient matrixes A_(k), B_(k) and D_(k) can be calculated.According to the OCV-SOC curve of the battery pack 101, coefficientmatrixes C_(k) can be obtained.

$A_{k} = \begin{bmatrix}1 & 0 & 0 \\0 & ^{- \frac{T}{\tau_{e}{(k)}}} & 0 \\0 & 0 & ^{- \frac{T}{\tau_{d}{(k)}}}\end{bmatrix}$ $B_{k} = \begin{bmatrix}{{- k_{\eta}}{T/Q_{0}}} \\{R_{e}\left( {1 - ^{- \frac{T}{\tau_{e}{(k)}}}} \right)} \\{R_{d}\left( {1 - ^{- \frac{T}{\tau_{d}{(k)}}}} \right)}\end{bmatrix}$ $C_{k} = \begin{bmatrix}\left. \frac{\partial U_{oc}}{\partial{SOC}} \right|_{{SOC} = {S\hat{O}{C{(K)}}^{-}}} & {- 1} & {- 1}\end{bmatrix}^{T}$ D_(k) = −R₀(k)

Step 2: Initiating the Variable of State

In this disclosure, the initiation of the variable of state comprisesinitiating three components of X_(k-1) ⁺ with SOC*(k), 0, 0,respectively, and initiating P_(k-1) ⁺ with the varance of X_(k-1) ⁺,i.e., var(X_(k-1) ⁺), as following:

X_(k-1) ⁺=[SOC*(k) 0 0]^(T)

P_(k-1) ⁺=var(X_(k-1) ⁺)

Here, SOC*(k) is the result obtained at step S505.

Step 3: EKF Iteration

The following expression 2-15 is an EKF iteration formula:

$\begin{matrix}\left\{ \begin{matrix}{X_{k}^{-} = {{A_{k}P_{k - 1}^{+}} + {B_{k}{I(k)}}}} \\{P_{k}^{-} = {{A_{k}P_{k - 1}^{+}A_{k}^{T}} + D_{W}}} \\{L_{k} = {P_{k}^{-}{C_{k}^{T}\left( {{C_{k}P_{k}^{-}C_{k}^{T}} + D_{v\;}} \right)}^{- 1}}} \\{X_{k}^{+} = {X_{k}^{-} + {L_{k}\left( {U_{k} - {U(k)}} \right)}}} \\{P_{k}^{+} = {\left( {1 - {L_{k}C_{k}}} \right)P_{k}^{-}}}\end{matrix} \right. & \left( {2\text{-}15} \right)\end{matrix}$

In the expression 2-15, U_(k) is the voltage obtained at the measurementstep S504, P_(k) is mean squared estimation error matrix at time pointk, L_(k) is the Kalman system gain, D_(w) and D_(v) stand respectivelyfor system noises and measurement noises, which are determined by noisesof practical systems. In the exemplary disclosure, the system noiseD_(w) and measurement noise D_(v) are both set as normal distributionnoises with mean of 0 and squared error of 0.1.

Iterating with the expression 2-15, a best variable of state would beachieved: X_(k) ⁺=[SOC(k) U_(e)(k) U_(d)(k)]^(T). According to the bestvariable of state, a best state of charge, SOC(, can be retrieved.

While the foregoing description and drawings represent the preferredembodiments of the present invention, it will be understood that variousadditions, modifications and substitutions may be made therein withoutdeparting from the spirit and scope of the present invention as definedin the accompanying claims. In particular, it will be clear to thoseskilled in the art that the present invention may be embodied in otherspecific forms, structures, arrangements, proportions, and with otherelements, materials, and components, without departing from the spiritor essential characteristics thereof The presently disclosed embodimentsare therefore to be considered in all respects as illustrative and notrestrictive, the scope of the invention being indicated by the appendedclaims, and not limited to the foregoing description.

What is claimed is:
 1. A SOC estimation method applied to a batterysystem device comprising a battery pack, the SOC estimation methodcomprising a plurality of SOC estimation processes each futhercomprising: determining an initial SOC value; determining whether thebattery pack is in a working status; measuring the voltage and currentof the battery pack if the battery pack is in the working statuscalculating a current SOC value by using an ampere-hour method based onthe initial SOC value and the measured voltage and current; determiningdynamic characteristic parameters of the battery pack; and optimizingthe current SOC value by using extended Kalman filter (EKF) method andbased on the dynamic characteristic parameters of the battery pack. 2.The SOC estimation method of claim 1, wherein determining whether thebattery pack is in the working status comprises determining whether thebattery pack is charging or discharging.
 3. The SOC estimation method ofclaim 1, wherein the step of determining the initial SOC valuecomprises: determining whether an idle time of the battery pack islonger than a predefined time period; reading a previous SOC valuegenerated during a previous SOC estimation process if the idle time ofthe battery pack is not longer than the predefined time period, anddetermining the previous SOC value as the initial SOC value; anddetermining the initial SOC based on an OCV-SOC mapping table of thebattery pack if the idle time of the battery pack is longer than thepredefined time period.
 4. The SOC estimation method of claim 3, whereinthe predefined time period is one hour.
 5. The SOC estimation method ofclaim 3, wherein the OCV-SOC mapping table of the battery pack isachieved by using the following steps: keeping battery units of thebattery pack under a status without charging or discharging over onehour; discharging the battery unit continuously lasting for 900 seconds;and keeping the battery unit under the status without charging ordischarging for relatively long time.
 6. The SOC estimation method ofclaim 3, wherein the idle time of the battery pack is the time durationof the battery pack without charging or discharging activities.
 7. TheSOC estimation method of claim 3, wherein the OCV-SOC mapping table ofthe battery pack is established by: A) charging the battery pack fullyand completely; B) placing the battery pack in an idle status, withoutcharging or discharging, for over one hour; C) discharging the batterypack to reduce 5 percent of the SOC of the battery pack by using aprogrammable electronic load, recording the open circuit voltage of thebattery pack and subsequently placing the battery pack in the idle statefor over one hour; D) repeating said step C), under constant temperatureof substantially 20 degree Celsius, until the battery pack dischargescompletely; and E) establishing the OCV-SOC mapping table based on theopen circuit voltages and corresponding SOC values of the battery packrecorded in step C) and step D).
 8. The SOC estimation method of claim1, wherein the dynamic characteristic parameters of the battery pack isdetermined in each SOC estimation process based on dynamiccharacteristic parameter obtained in a previous SOC estimation processand the measured voltage and current.
 9. The SOC estimation method ofclaim 1, wherein the step of optimizing the current SOC value by usingextended Kalman filter method comprises: determining the linearcoefficient of the variable of state based on the dynamic characteristicparameters of the battery pack; initiating the variable of state; anditerating using the EKF method.
 10. A SOC estimation system in a batterysystem device comprising a battery pack, the SOC estimation systemcomprising a controller and relevant storage unit, the storage unitstoring a plurality of executable programs, the controller executing theprograms to reach the functions including: determining an initial SOCvalue; determining whether the battery pack is in a working status;measuring the voltage and current of the battery pack if the batterypack is in the working status; calculating a current SOC value by usingan ampere-hour method based on the initial SOC value and the measuredvoltage and current; determining dynamic characteristic parameters ofthe battery pack; and optimizing the current SOC value by using extendedKalman filter (EKF) method and based on the dynamic characteristicparameters of the battery pack.
 11. The SOC estimation system of claim10, wherein the battery pack is in the working status comprises thebattery pack is charging or discharging.
 12. The SOC estimation systemof claim 1, wherein the function of determining the initial SOC valuecomprises: determining whether an idle time of the battery pack islonger than a predefined time period; reading a previous SOC valuegenerated during a previous SOC estimation process if the idle time ofthe battery pack is not longer than the predefined time period, anddetermining the previous SOC value as the initial SOC value; anddetermining the initial SOC based on an OCV-SOC mapping table of thebattery pack if the idle time of the battery pack is longer than thepredefined time period.
 13. The SOC estimation method of claim 12,wherein the predefined time period is one hour.
 14. The SOC estimationmethod of claim 12, wherein the OCV-SOC mapping table of the batterypack is achieved by using the following steps: keeping battery units ofthe battery pack under a status without charging or discharging over onehour; discharging the battery unit continuously lasting for 900 seconds;and keeping the battery unit under the status without charging ordischarging for relatively long time.
 15. The SOC estimation method ofclaim 12, wherein the idle time of the battery pack is the time durationof the battery pack without charging or discharging activities.
 16. TheSOC estimation method of claim 12, wherein the OCV-SOC mapping table ofthe battery pack is established by: A) charging the battery pack fullyand completely; B) placing the battery pack in an idle status, withoutcharging or discharging, for over one hour; C) discharging the batterypack to reduce 5 percent of the SOC of the battery pack by using aprogrammable electronic load, recording the open circuit voltage of thebattery pack and subsequently placing the battery pack in the idle statefor over one hour; D) repeating said step C), under constant temperatureof substantially 20 degree Celsius, until the battery pack dischargescompletely; and E) establishing the OCV-SOC mapping table based on theopen circuit voltages and corresponding SOC values of the battery packrecorded in step C) and step D).
 17. The SOC estimation method of claim10, wherein the dynamic characteristic parameters of the battery pack isdetermined in each SOC estimation process based on dynamiccharacteristic parameter obtained in a previous SOC estimation processand the measured voltage and current.
 18. The SOC estimation method ofclaim 10, wherein the function of optimizing the current SOC valuecomprises: determining the linear coefficient of the variable of statebased on the dynamic characteristic parameters of the battery pack;initiating the variable of state; and iterating using the EKF method.